Apart from strengthening the evidence in favour of the existence of the Reuter fixed point, we can also give a straightforward argument in favour of the theory being unitary, since the terms that contain four derivatives are redundant.
This property will be true of all higher derivatives if the fixed point can be found in the minimal essential scheme, which assumes their absence from the beginning. Consequently, the minimal essential scheme provides a frame work to address some of the open problems for the asymptotic safety program [1]}, [2]} which concern the form of the propagator.
We should stress that
by using the minimal essential scheme we can dictate which physical degrees of freedom we are attempting to renormalise, and, thus, ensure that we are dealing with a unitary theory, rather than searching in a space of theories littered with non-unitary ones. In calculations that retain terms outside of those in the minimal essential scheme, we expect to find many fixed points which lie in different universality classes. Indeed, studies that include many powers of the Riemann curvature have found fixed points with as many as four relevant directions [3]}.
